Seasonal dynamics and thresholds governing recurrent epidemics

Driven by seasonality, many common recurrent infectious diseases are characterized by strong annual, biennial and sometimes irregular oscillations in the absence of vaccination programs. Using the seasonally forced SIR epidemic model, we are able to provide new insights into the dynamics of recurrent diseases and, in some cases, specific predictions about individual outbreaks. The analysis reveals a new threshold effect that gives clear conditions for the triggering of future disease outbreaks or their absence. The threshold depends critically on the susceptibility S (0) of the population after an outbreak. We show that in the presence of seasonality, forecasts based on the susceptibility S (0) are more reliable than those based on the classical reproductive number R (0) from the conventional theory.